What is the foci 16x^2-y^2-64x-2y+47=0 ?

The foci 16x^2-y^2-64x-2y+47=0 is (2+sqrt(17),-1),(2-sqrt(17),-1)

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foci 16x^2-y^2-64x-2y+47=0

foci

16 x^{2} - y^{2} - 64 x - 2 y + 47 = 0

(2 + 17, - 1), (2 - 17, - 1)

Solution steps

(h + c, k), (h - c, k)

Calculate Hyperbola properties

16 x^{2} - y^{2} - 64 x - 2 y + 47 = 0 :

Right-left Hyperbola with

(h, k) = (2, - 1), a = 1, b = 4

(2 + c, - 1), (2 - c, - 1)

Compute

c :

c = 1^{2} + 4^{2} : 17

(2 + 17, - 1), (2 - 17, - 1)

\frac{( x - 1 ) ^{2}}{16} - \frac{( y - 7 ) ^{2}}{20} = 1

y^{2} - 9 x^{2} - 8 y - 54 x - 81 = 0

\frac{( x - 3 ) ^{2}}{8 ^{2}} - \frac{( y - 2 ) ^{2}}{8 ^{2}} = 1

\frac{x ^{2}}{49} - \frac{y ^{2}}{81} = 1

\frac{y ^{2}}{6} - \frac{x ^{2}}{11} = 1

What is the foci 16x^2-y^2-64x-2y+47=0 ?
The foci 16x^2-y^2-64x-2y+47=0 is (2+sqrt(17),-1),(2-sqrt(17),-1)